<h2>Problem 87</h2>
<div style="color:#666;font-size:80%;">21 January 2005</div><br />
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<p>The smallest number expressible as the sum of a prime square, prime cube, and prime fourth power is 28. In fact, there are exactly four numbers below fifty that can be expressed in such a way:</p>
<p style='margin-left:50px;'>28 = 2<img src="" style="display:none;" alt="^(" /><sup>2</sup><img src="" style="display:none;" alt=")" /> + 2<img src="" style="display:none;" alt="^(" /><sup>3</sup><img src="" style="display:none;" alt=")" /> + 2<img src="" style="display:none;" alt="^(" /><sup>4</sup><img src="" style="display:none;" alt=")" /><br />
33 = 3<img src="" style="display:none;" alt="^(" /><sup>2</sup><img src="" style="display:none;" alt=")" /> + 2<img src="" style="display:none;" alt="^(" /><sup>3</sup><img src="" style="display:none;" alt=")" /> + 2<img src="" style="display:none;" alt="^(" /><sup>4</sup><img src="" style="display:none;" alt=")" /><br />
49 = 5<img src="" style="display:none;" alt="^(" /><sup>2</sup><img src="" style="display:none;" alt=")" /> + 2<img src="" style="display:none;" alt="^(" /><sup>3</sup><img src="" style="display:none;" alt=")" /> + 2<img src="" style="display:none;" alt="^(" /><sup>4</sup><img src="" style="display:none;" alt=")" /><br />
47 = 2<img src="" style="display:none;" alt="^(" /><sup>2</sup><img src="" style="display:none;" alt=")" /> + 3<img src="" style="display:none;" alt="^(" /><sup>3</sup><img src="" style="display:none;" alt=")" /> + 2<img src="" style="display:none;" alt="^(" /><sup>4</sup><img src="" style="display:none;" alt=")" /></p>
<p>How many numbers below fifty million can be expressed as the sum of a prime square, prime cube, and prime fourth power?</p>

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